Abstract
We establish the boundedness of martingale transforms on Banach function spaces by using the Rubio de Francia extrapolation theory and the interpolation theorem by Zygmund. The main result also yields the boundedness of the martingale transforms on rearrangement-invariant Banach function spaces, Orlicz spaces, Lorentz-Karamata spaces, Zygmund spaces, Lebesgue spaces with variable exponents, Morrey spaces with variable exponents and Lorentz-Karamata Morrey spaces. Copyright © 2022 the Author(s), licensee AIMS Press.
| Original language | English |
|---|---|
| Pages (from-to) | 2247-2262 |
| Journal | Electronic Research Archive |
| Volume | 30 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Apr 2022 |
Citation
Ho, K.-P. (2022). Martingale transforms on Banach function spaces. Electronic Research Archive, 30(6), 2247-2262. doi: 10.3934/era.2022114Keywords
- Martingale transform
- Banach function spaces
- Orlicz spaces
- Lorentz-Karamata spaces
- Variable Lebesgue spaces
- Morrey spaces